The Luck of the Draw

There’s a remarkable pairing in the first round of the U.S. Open tennis tournament. At noon tomorrow (August 27), Grigor Dimitrov plays Stan Wawrinka, just two months after they happened to draw each other in the first round of Wimbledon (Wawrinka won).

Both Dimitrov and Wawrinka are among the elite of men’s tennis, and it’s matchups like this one that most tourneys are designed to avoid through the use of seeding. But there’s always some degree of variance between the ATP point totals used by tournaments to make their seedings and the actual skill level of the players. Let’s take a close look at the details of this particular pairing.

Note, first, that the official seeding is kinder to Dimitrov than it is to Wawrinka. According to a summary of the betting odds, Wawrinka is the seventh favorite to win the tournament. Dimitrov is also respected by the punters, but not as highly – he’s the 13th favorite. I’ll assume here that the oddsmakers know their business, and that betting odds represent actual skill. If there were an obvious disconnect between betting odds and absolute skill, presumably betters would exploit it, and the bookies would go broke.

Dimitrov, however, is seeded 8 on the basis of his accumulated ATP points, which just qualifies him for fourth tier (5-8) seeding. Wawrinka, in contrast, has been injured until recently, and his ATP point totals have languished so much that he is ranked just outside the top 100. Wawrinka is not only not seeded in any tier, but received a wild card exemption from the tournament organizers in order to be accepted into the main draw without having to play qualifiers. Dimitrov is, then, over-seeded by a good measure, and Wawrinka is severely under-seeded.

Here’s what that means in terms of the two players’ expectations (measured in prize money) for the coming tourney.

If the tournament were perfectly seeded, Dimitrov could expect to win $276,819 as the 13th best player seeded in the sixth tier (13-16). But he’s seeded in the fourth tier (4-8), and that’s likely to give him a better draw. I simulated half a million playings of the tourney, with a new draw each time, and Dimitrov, by virtue of his better seeding, earned an average of $328,718, about 19%, to the good.

Wawrinka, in contrast suffers greatly from being unseeded. His expectation in a perfectly seeded tourney would be $$482,311, but unseeded he can expect only $358,662, about a 26% loss. He still expects to win more money than Dimitrov, but not that much more – not nearly enough more when you consider that he’s six places better than Dimitrov in the skill ranking.

Now, that’s the result on average across half a million simulated draws. But what is the expectation given the one draw that actually did happen?

The draw that actually happened is, for both Dimitrov and Wawrinka, a two-edged sword. Most obviously, they both got a really tough first round opponent. Most of the time, both players would draw someone much less skillful in the first round. But after that tough first round, whichever player survives has a pretty favorable path. In round 2, they’ll play a qualifier. After that, there are none of the really big names in their part of the bracket until they get to the quarterfinals.

My model has Wawrinka a 60% favorite to beat Dimitrov, and if he does get past Dimitrov, he’ll be nearly 50% to make it to the quarterfinals or beyond. So, notwithstanding the bad luck of drawing someone as good as Dimitrov in the first round, Wawrinka’s expectation is actually about 7% better than it is for the average of all possible draws. His expectation is now up to $382,935. That’s still almost $100K less than what he’d expect with perfect seeding, but it’s not as awful as it might have been.

For Dimitrov, however, drawing Wawrinka is a catastrophe. He, too, will benefit from weak opposition if he wins the first round. But with a 60% chance of earning only the $56,000 owing to first-round losers, his expectation plummets to $202,037.

But Dimitrov is only the second biggest loser in the draw. Federer’s expectation declines by more than $190K because he has some tricky early rounds and the prospect of meeting Djokovic in the quarterfinals. The biggest losers in percentage terms are Fuchsovic and Ferrer, decent players who had reasonable chances to progress a round or two until they drew Djokovic and Nadal, respectively, in round one.

The biggest winner in the draw is Nadal, +$111K, who avoids Djokovic until the final, and landed in a fairly benign part of the draw. Djokovic and Cilic also did quite well, at +$85K and +$80K.